For k0, either 1-sin(phi) or maybe generic published values for the soil type. Or if you know or measure in-situ horizontal and vertical effective stress, it's just the ratio. Poissons ratio is horizontal strain / vertical strain so not the same as K, one is about stresses and one is about strains.
K0 is the ratio of horizontal effective stress to vertical effective stress, at least as I understood it. I'm not sure k0 changes between drained and undrained conditions, but I suppose that the horizontal and vertical earth pressure might?